On the Sombor characteristic polynomial and Sombor energy of a graph

Abstract

Let G be a simple graph with vertex set V(G)={v1,v2,…,vn}. The Sombor matrix of G, denoted by ASO(G), is defined as the n×n matrix whose (i, j)-entry is d2i+d2j−−−−−−√ if vi and vj are adjacent and 0 for another cases. Let the eigenvalues of the Sombor matrix ASO(G) be ρ1≥ρ2≥⋯≥ρn which are the roots of the Sombor characteristic polynomial ∏ni=1(ρ−ρi). The Sombor energy ESO of G is the sum of absolute values of the eigenvalues of ASO(G). In this paper, we compute the Sombor characteristic polynomial and the Sombor energy for some graph classes, define Sombor energy unique and propose a conjecture on Sombor energy.